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Deep Boltzmann Machines: Rigorous Results at Arbitrary Depth

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The magnet feeders are part of the critical systems of a fusion reactor since they represent the interface between the in-cryostat components at 4.5 K and the room-temperature cryogenic plant and power supply. The European DEMO tokamak foresees 16 toroidal ...

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Hitting with Probability One for Stochastic Heat Equations with Additive Noise

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We study the hitting probabilities of the solution to a system of d stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive (d-6)\documentclass[12pt]{minimal} \usepackage{ ...

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Designing novel materials is greatly dependent on understanding the design principles, physical mechanisms, and modeling methods of material microstructures, requiring experienced designers with expertise and several rounds of trial and error. Although rec ...

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We study the statistical mechanics and the equilibrium dynamics of a system of classical Heisenberg spins with frustrated interactions on a d -dimensional simple hypercubic lattice, in the limit of infinite dimensionality d -> infinity . In the analysis we ...

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Modern integrated circuits are tiny yet incredibly complex technological artifacts, composed of millions and billions of individual structures working in unison. Managing their complexity and facilitating their design drove part of the co-evolution of mode ...

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Information theory has allowed us to determine the fundamental limit of various communication and algorithmic problems, e.g., the channel coding problem, the compression problem, and the hypothesis testing problem. In this work, we revisit the assumptions ...

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Plantar pressure plays a crucial role in the pathogenesis of foot ulcers among patients with diabetes and peripheral polyneuropathy. Pressure relief is a key requirement for both the prevention and treatment of plantar ulcers. Conventional medical practice ...

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Global existence for perturbations of the 2D stochastic Navier-Stokes equations with space-time white noise

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We prove global in time well-posedness for perturbations of the 2D stochastic Navier-Stokes equations partial derivative( t)u + u center dot del u = Delta u - del p + sigma + xi, u(0, center dot ) = u(0),div (u) = 0, driven by additive space-time white noi ...

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Deep learning has emerged as a promising avenue for automatic mapping, demonstrating high efficacy in land cover categorization through various semantic segmentation models. Nonetheless, the practical deployment of these models encounters important challen ...

Ieee-Inst Electrical Electronics Engineers Inc2024